An issue can occur in iOS where text messages stop sending to a contact and their display name will displayed as “Name Buddy” (even if you correctly choose them and their name displayed when selecting the recipient). Additionally, if they have no contact photo you also won’t see their first and last initial in the avatar circle.
Many articles will suggest that logging out of your iCloud account, rebooting and logging back in will fix the issue but that isn’t always the case.
The Fix: The quickest fix with the least amount of risk is deleting the contact for that individual and then creating a new one for them.
Although fix applies to many iOS versions it was last tested on iOS 15.2.